电荷泵锁相环的非线性分析：保持和引入范围
Nonlinear analysis of charge-pump phase-locked loop: the hold-in and pull-in ranges
摘要：
本文研究了CP-PLL的一个比较完整的数学模型，它的可靠性足以作为可靠分析这类电路动态特性的工具。我们完善相关的数学定义的保持和拉入范围相关的局部和全局稳定性。电荷泵锁相环稳态的稳定性分析是不平凡的：可用的CP-PLL模型的直接线性化可能会导致不正确的结论，因为系统在稳态附近不平滑，可能会过载。在这项工作中，必要的局部稳定性分析的细节，并计算保持范围。通过极限环的分析，得到了拉入范围的上限估计。该研究回答了Gardner关于CP-PLL与等效经典PLL瞬态响应相似性的猜想，以及关于带比例积分滤波器的CP-PLL的无限拉入范围的理论。
英文摘要：
In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as a tool for credible analysis of dynamical properties of these circuits, is studied. We refine relevant mathematical definitions of the hold-in and pull-in ranges related to the local and global stability. Stability analysis of the steady state for the charge-pump phase locked loop is non-trivial: straight-forward linearization of available CP-PLL models may lead to incorrect conclusions, because the system is not smooth near the steady state and may experience overload. In this work necessary details for local stability analysis are presented and the hold-in range is computed. An upper estimate of the pull-in range is obtained via the analysis of limit cycles. The study provided an answer to Gardner's conjecture on the similarity of transient responses of CP-PLL and equivalent classical PLL and to conjectures on the infinite pull-in range of CP-PLL with proportionally-integrating filter.
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